147ed12

← 146ed12

147ed12

148ed12 →

Prime factorization	3 × 72
Step size	29.265 ¢
Octave	41\147ed12 (1199.87 ¢) (convergent)
Twelfth	65\147ed12 (1902.23 ¢) (semiconvergent)
Consistency limit	16
Distinct consistency limit	10

147 equal divisions of the 12th harmonic (abbreviated 147ed12) is a nonoctave tuning system that divides the interval of 12/1 into 147 equal parts of about 29.3 ¢ each. Each step represents a frequency ratio of 12^1/147, or the 147th root of 12.

Theory

65edt is almost identical to 41edo, but with the 3/1 rather than the 2/1 being just. The octave is about 0.3053 cents compressed. Like 41edo, 65edt is consistent to the 16-integer-limit.

Harmonics

Approximation of harmonics in 65edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-0.3	+0.0	-0.6	-6.5	-0.3	-3.8	-0.9	+0.0	-6.8	+3.7	-0.6
	Relative (%)	-1.0	+0.0	-2.1	-22.3	-1.0	-13.1	-3.1	+0.0	-23.4	+12.7	-2.1
Steps (reduced)		41 (41)	65 (0)	82 (17)	95 (30)	106 (41)	115 (50)	123 (58)	130 (0)	136 (6)	142 (12)	147 (17)

Approximation of harmonics in 65edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23	24
Error	Absolute (¢)	+7.1	-4.1	-6.5	-1.2	+10.9	-0.3	-6.1	-7.1	-3.8	+3.4	+14.2	-0.9
	Relative (%)	+24.3	-14.1	-22.3	-4.2	+37.1	-1.0	-20.9	-24.4	-13.1	+11.7	+48.7	-3.1
Steps (reduced)		152 (22)	156 (26)	160 (30)	164 (34)	168 (38)	171 (41)	174 (44)	177 (47)	180 (50)	183 (53)	186 (56)	188 (58)

See also

• 24edf – relative edf
• 41edo – relative edo
• 65edt – relative edt
• 95ed5 – relative ed5
• 106ed6 – relative ed6
• 361ed448 – close to the zeta-optimized tuning for 41edo